Question

Figure ABCD is a rectangle. The length of segment AE is (5x − 7) units and the length of segment EC is (2x − 1) units.

What is the length of diagonal BD?

8 units
6 units
12 units
10 units

Answer 1

Hello!

To find our answer, we will first want to find x. Our two line segments appear to be congruent. If we add them up, it will be equal to BD, so let's find x, plug it in, and add it up.

5x-7=2x-1

Let's subtract 2x from both sides.

3x-7=-1

We add 7 to both sides.

3x=6

We divide both sides by 3.

x=2

Now, let's plug it in to both equations.

5(2)-7

10-7

3

2(2)-1

4-3=3

3+3=6

Therefore, our answer is
`\boxed {B) 6 units}`

I hope this helps!